This need to be solved for insertion deletion and rotations step by step **Exercise 5: Constructing and Modifying an AVL Tree***Objective*: Demonstrate the process of inserting a series of numbers into an empty AVL tree, followed by deleting the root and replacing it with the smallest key in the right subtree. Document each step with the corresponding tree structure and specify the type of rotation, if any.*Instructions*: Insert the numbers 9, 1, 2, 8, 10, 5, 4, 3, 7, 6 into an initially empty AVL tree. After all insertions, delete the root, replacing it with the smallest key from its right subtree. For each insertion, deletion, and rotation, illustrate the AVL tree and indicate the type of rotation performed (e.g., left rotation, right rotation, left-right rotation, or right-left rotation).*Steps*:1. **Insertions**: - Start by inserting 9. - Continue with 1, 2, 8, 10, 5, 4, 3, 7, and 6. - After each insertion, check if the tree requires balancing. - If balancing is needed, identify and execute the appropriate rotation.2. **Deletion**: - Remove the root node. - Replace it with the smallest key from the right subtree. - After deletion, if the tree becomes unbalanced, perform necessary rotations to restore the AVL property.*Outcome*: The final balanced AVL tree will reflect all the transformations following the above operations, demonstrating an efficient method for maintaining balance and optimizing search operations in a binary tree.

Answered: Show the process of inserting 9, 1, 2,…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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This need to be solved for insertion deletion and rotations step by step

**Exercise 5: Constructing and Modifying an AVL Tree**

*Objective*: Demonstrate the process of inserting a series of numbers into an empty AVL tree, followed by deleting the root and replacing it with the smallest key in the right subtree. Document each step with the corresponding tree structure and specify the type of rotation, if any.

*Instructions*: Insert the numbers 9, 1, 2, 8, 10, 5, 4, 3, 7, 6 into an initially empty AVL tree. After all insertions, delete the root, replacing it with the smallest key from its right subtree. For each insertion, deletion, and rotation, illustrate the AVL tree and indicate the type of rotation performed (e.g., left rotation, right rotation, left-right rotation, or right-left rotation).

*Steps*:
1. **Insertions**:
- Start by inserting 9.
- Continue with 1, 2, 8, 10, 5, 4, 3, 7, and 6.
- After each insertion, check if the tree requires balancing.
- If balancing is needed, identify and execute the appropriate rotation.

2. **Deletion**:
- Remove the root node.
- Replace it with the smallest key from the right subtree.
- After deletion, if the tree becomes unbalanced, perform necessary rotations to restore the AVL property.

*Outcome*: The final balanced AVL tree will reflect all the transformations following the above operations, demonstrating an efficient method for maintaining balance and optimizing search operations in a binary tree.

Expert Solution

Inserting into list

Insert 9 and then Insert 1

Insert 2 if inserted at right of 1 AVL Tree condition violates at root. Perform right rotation

Insert 8

Insert 10

Inserting 5 makes unbalanced perform left rotation

Inserting 4

Inserting 3 makes unbalanced perform right rotation

Insert 7 makes unbalanced at root perform left rotation

Insert 6 unbalanced at root perform left rotation

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Show the process of inserting 9, 1, 2, 8, 10, 5, 4, 3, 7, 6 into an initially empty AVL tree. Then the root is deleted and replaced by the smallest key in the right subtree. Show the tree after each insertion, deletion, and rotation. Indicate the type of each rotation.